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Confusing but simple cyclic hexagon (ae || bd, bc || df)

Source: 1st German pre-TST 2006, problem 1

December 5, 2005
geometrygeometric transformationreflectiongeometry proposed

Problem Statement

Let AA, BB, CC, DD, EE, FF be six points on a circle such that AE∥BDAE\parallel BD and BC∥DFBC\parallel DF. Let XX be the reflection of the point DD in the line CECE. Prove that the distance from the point XX to the line EFEF equals to the distance from the point BB to the line ACAC.
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